Example of CA using Markov Chain

To illustrate the technique of modelling landcover change by CA, we will present a relatively simple but effective model that combines cellular automata spatial rules with Markov chain transition rules. For example, this approach is proposed as a module called MARKOV / CA_MARKOV in the raster GIS IDRISI (Eastman 2008). The procedure models predictive termLand Use Cover (LUC) changes within two stages

Stage 1

A termMarkov chain analysis (MARKOV) is performed in order to estimate the transition matrix between the two past and documented dates (date 1 and date 2) and to estimate probabilities of change for the third date (date 3) to be predicted. Input and output parameters for this analysis are the following:

Stage 2

A Cellular automata predicting model (CA_MARKOV) estimates the spatial distribution of landcover at a later date (date 3):


The data used in this illustration are landcover map layers of 1952, 1974 and 1993 for the town of Bulle in the canton of Fribourg in Switzerland. As already previously commented, this dataset has been developed by K. Al-Ghamdi in the context on his PhD research work on LUCC modelling (Al-Ghamdi 2008). The objective of this illustration was to analyse the LUC change during the period from 1952 to 1974 and based on this modelling to predict the evolution for the date 1993. The ground truth 1993 LUC layer will then be used to assess the performance of the procedure. As already illustrated in figure 3.4 for the dates 1946 and 2001, six categories of landcover are identified: lake/pond, river, wetland/marshland, forest, agricultural/open field and urban. Linear features, such as the road network, were not included into the analysis as the 10m resolution of the LUC would overestimate its impact and development.

Observed land cover (LUC) distribution in 1962, 19974 and 1993
Simulation of the land cover (LUC) distribution in 1993 with the use of a model combining Markov chain transition rules and cellular automata spatial rules (MARKOV / CA_MARKOV) and based on 1952-1974 development. A mask is applied for restricting protected areas from further changes

Several comments can be made about this spatial modelling of LUCC:


Among other limitations one should identify the inability to take into account the influence of the road network that could potentially generate new “seeds” of development.